Although blind, adaptive algorithms for equalization are widely studied, hitherto there has been little academic attention given to blind, adaptive algorithms for channel shortening. Channel shortening is needed to preserve subcarrier orthogonality in multicarrier modulation, and it can be used to dramatically reduce the complexity of maximum likelihood sequence estimation and multiuser detection. This paper reviews the channel shortening problem from a tutorial perspective, and shows how it is an extension of traditional equalization. It is shown that traditional methods of devising blind, adaptive equalization algorithms cannot be easily applied to the channel shortening problem. The paper concludes with a discussion of several new property restoral algorithms that enable blind, adaptive channel shortening.